2.4 整数、有理数与实数
1.单词，词组，短语翻译
(1)整数 integer，有理数rational number，无理数irrational number，实数real number，负数negative number, 相反数the negative，实直线real line，实轴real axis，尺度scale在……的左边/右边 to the left/right of (2)和sum，差difference怎样才能壮阳，积product，商quotient，幂送别的歌曲power房门，不等式 inequality (3) 公理axiom，序公理the order axiom，域公理the field axiom (4)有序的ordered,完整的英文微信名字entirely complete,欧式的Euclidean,适当的appropriate,显著的distinguished,清晰的illuminating (5)可推导的公式deducible formula，可互相交换的运算interchangeable operation，采用一组公理to adopt a t of axioms，对应于某个对象corresponding to an object / to correspond to a particular object，用数学归纳法证明proof by induction，对检验结论的有效性很有用a very worthwhile aid to test the validity of conclusions， 把这两个集加以区别to distinguish the two ts
2. 汉译英
（1）严格说，这样描述整数是不完整的，因为我们并没有说明“以此类推”或“反复加 1” 的含义是什么。
Strictly speaking,，this description of the positive integers is not entirely complete becau we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.
（2）两个整数的和、差或积是一个整数，但是两个整数的商未必是一个整数。
The sum, difference, or product of two integers is an integer, but the quotient of two integers need not be an integer.
（3） 这种用几何来表示实数的办法对于帮助我们更好地发现与理解实数的性质是非常有价值的。
This device for reprenting real numbers geometrically is a very worthwhile aid that helps us to discover and understand better certain properties of real numbers.
1999年五行属什么
（4）几何经常为一些特定的定理提供证明思路（建议） ，而且，有时几何的论证比纯分析的 （完全依赖于实数公理的）证明更清晰。
The geometry often suggests the method of proof of a particular theorem, and sometimes a geometric argument is more illuminating than a purely analytic proof (one depending entirely on the axioms for the real numbers).
（5）一个由实数组成的集若满足如下条件则称为开区间（open interval） 。
If a t consisting of real numbers satisfies the following conditions we call it an open interval.
（6）实数 a 是-a 的相反数，它们的绝对值相等，且当 a ≠ 0 时，其符号不同。
The real number a is the negative number of –a and their absolute values are equal. When a ≠ 0, their notations are different.
（7）每个实数刚好对应着实轴上的一点，反之，对实轴上的每一点，有且只有一个实数与之对应。
Each real number corresponds to exactly one point on this line and, converly, each point on the line corresponds to one and only one real number.
（8）在几何上，实数之间的次序关系可以在数轴上清楚地表示出来。
In geometry, the ordering relation among the real numbers can be expresd clearly in real axis.
3. 英译汉
梦回童年（1）A common mistake is to think that –x is a negative number .But –x can be positive ,O,or negative ,depending on the value of x. 人们通常错误地认为 –x是一个负数，但是-x可以是正数，0或者负数，取决于x的取值。
（2遗愿清单影评）Each property that we covered in the last ction involves only one operation ,such as ab=ba and 0+a=a.We now consider a property that links addition and multiplication.It is called the distributive property or multiplication distributive over addition and is illustrated with the following formulas : a(b+c)=ab + bc; (b+c)a=ba+ca. 我们在上一节所
讲到的每一种特性只包括了一种运算，比如 ab=ba, 0+a=a。我们现在所考虑的一种特性是把加法和乘法连结起来， 被叫做（乘法）分配率，或者叫做在加法上的乘法分配率，用下面的公式来举例说明：a(b+c)=ab + bc; (b+c)a=ba+ca
(3)Consider the decimal formed by writing the natural numbers in order: .123456789101112131415… Since the natural numbers do not terminate or repeat ,this is a nonterminating nonrepeating decimal.The decimal which cannot be converted to the ration of two integers is called irrational number.This t of numbers is denoted by the symbol H,and H={x：x is a nonterminating nonrepeating decimal}. 思考这样的小数，它是由按顺序写出来的自然数组成的，.123456789101112131415… 因为这些自然数没有终结，或者不重复，所以这种小数叫做无限不循环小数。这种不能被转换成两个整数比率的小数叫做无理数。无理数的集合用大写字母H表示，如下所示：H={x语文作文600字：x是一个无限不循环小数}。
